Decentralized robust control of uncertain Markov jump parameter systems via output feedback

  • Authors:

  • Li Li;Valery A. Ugrinovskii;Robert Orsi

  • Affiliations:

  • School of Information Technology and Electrical Engineering, University of New South Wales at the Australian Defence Force Academy, ADFA, Canberra, ACT 2600, Australia;School of Information Technology and Electrical Engineering, University of New South Wales at the Australian Defence Force Academy, ADFA, Canberra, ACT 2600, Australia;Research School of Information Sciences and Engineering, The Australian National University, Canberra, ACT 0200, Australia

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2007

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Abstract

This paper addresses the problem of decentralized robust stabilization and control for a class of uncertain Markov jump parameter systems. Control is via output feedback and knowledge of the discrete Markov state. It is shown that the existence of a solution to a collection of mode-dependent coupled algebraic Riccati equations and inequalities, which depend on certain additional parameters, is both necessary and sufficient for the existence of a robust decentralized switching controller. A guaranteed upper bound on robust performance is also given. To obtain a controller which satisfies this bound, an optimization problem involving rank constrained linear matrix inequalities is introduced, and a numerical approach for solving this problem is presented. To demonstrate the efficacy of the proposed approach, an example stabilization problem for a power system comprising three generators and one on-load tap changing transformer is considered.